Methods and system for nonintrusive load monitoring

ABSTRACT

Identification and tracking of major electric appliances by using aggregate power data obtained at the main breaker level of a residence or commercial establishment. Step power changes and power surges characterize appliances. These features are identified and the time of use and duration statistics are considered to match an observed sequence of power changes with the appliances being turned on and off. The time-dependent usage of appliances and their power consumption are then reconstructed.

RELATED APPLICATIONS

This application is a U.S. National Stage application based onInternational Application No. PCT/US2011/064745, filed Dec. 13, 2011,which claims priority under 35 U.S.C. §119(e) to United StatesProvisional Application Ser. No. 61/422,315, filed Dec. 13, 2010, thecontents both of which are incorporated herein by reference in theirentireties.

FIELD OF THE INVENTION

This invention relates to the field of monitoring and managingelectrical power utilization in residential and commercial settings.More particularly, it relates to nonintrusive load monitoring in whichaggregated power consumption data for a residential or commercialpremise is disaggregated for use in connection with energy management.

BACKGROUND

There is widespread recognition that significant savings in electricalenergy consumption can be achieved by better energy management andcontrol in residential and commercial buildings. To achieve moreefficient energy control, it would be helpful to have reasonablyaccurate real-time monitoring of the electrical loads (e.g., appliances,lighting devices, motors, etc.) in use. (Hereafter, the species term“appliance” is used interchangeably with the generic term “load,” unlessthe context indicates a specific type of appliance is intended.) One wayto obtain load-specific information about energy utilization is tomonitor each load individually. However, this requires that energy usagebe monitored at each appliance, either with apparatus internal to theappliance (thus raising the cost per appliance, especially to retrofitalready installed appliances) or requiring an add-on device perappliance. Another way is to monitor total electricity consumption inthe aggregate, at the main breaker or service feed level, and thendisaggregating the data to separate out the timing and contribution ofeach load of interest. Armed with that information, attention can begiven to more efficient usage of electrical energy, such as the savingsthat can be achieved by taking various steps (from changing an applianceto another model or time-shifting the use of an appliance, to any of anumber of other measures). However, disaggregating the overall energyconsumption into its constituent parts is a non-trivial task.

Such nonintrusive appliance load monitoring (NIALM) methods require bothhardware (including a sensor and other elements) and software (i.e.,signal processing algorithms executing on one or more processors)components. The software component of NIALM depends on the hardwarecomponent. For example, signal waveform analysis can be used if thesensor samples voltage and current at a rate of at least several kHz.However, such sensors are still expensive and not widely accessible. Aninexpensive and easy-to-install hardware alternative is a sensor thatmeasures the total electric power being delivered to a residential orcommercial premise at a sampling frequency of about 1 Hz. NIALMalgorithms corresponding to such sensor have been detailed in, forexample, U.S. Pat. Nos. 4,858,141; 5,717,325; 5,483,153 and in severalacademic publications. These algorithms detect step changes in power andmatch these changes with the loads being turned on or off. The changesin power can either be one-dimensional (e.g., only real power ismeasured) or two-dimensional (e.g., both real and reactive powercomponents are measured).

Even though these NIALM algorithms are capable of monitoring majorhousehold appliances and the like, their accuracy level is only in theneighborhood of 80%. The main reason for the monitoring accuracy beingthat low is that two or more different loads may be operatedconcurrently and even may be switched on or off in very close timeproximity. Further, the amount of power two different loads consumecould be quite similar. For example, the power draw of a computermonitor could approximately equal that of an incandescent bulb, whichmakes these two loads indistinguishable by the mentioned algorithms.Another significant cause for the low accuracy is that the mentionedalgorithms consider one-for-one matching between a power change and theswitching of a load state. This matching is prone to both measurementand algorithmic errors and to the ambiguity which results from asimultaneous starting or stopping of multiple loads.

Accordingly, a need exists for a NIALM system and method that canprovide more accurate appliance (load) usage data.

SUMMARY

A new set of NIALM systems and methods (i.e., algorithms) shown hereinis capable of significantly overcoming the above-noted challenges andaddressing the observed need. There are three main advantages to thesemethods. First, not only load state changes but also power surges(statistics of surge amplitude and duration) and their statisticaldistributions are used in order to more accurately identify loads andtheir energy consumption. Second, statistics of time of use (in terms ofboth duration and time of day) are utilized for better applianceidentification and matching with energy consumption. Third, the matchingbetween the measured power observations and the appliances at thepremise is made by consideration of those series of transitions amongthe appliance states which are possible, which maximizes the likelihoodof correctly determining not only the given series of power changes butalso the time-of-use statistics and power surge statistics.

In some embodiments, time statistics for power changes in the aggregated(common) power feed are estimated using historical data obtainedempirically or from another source, based on a relatively “long” timeinterval. The aggregated power change data is reprocessed using thosestatistics, to cluster tuples of power changes (pairs, triples, etc.)which, statistically, would appear likely to be attributable to the sameload. Using a Viterbi algorithm or similar technique, similar clustersthen are merged, overlapping clusters are better separated and the timestatistics are updated to estimate the times the loads appear to be indifferent states. Based on the updated statistics, real-timepower-change measurements are then processed the same way, to clusterdetected changes and develop real-time load state information. Toassociate that information with identifiable loads, one may correlateknown load actions with the estimates (e.g., by logging at least onetime a load is known to have been turned on and/or off and matchingthose actions to observed power changes).

Some embodiments involve a method for nonintrusive monitoring ofelectrical energy usage by a plurality of electrical loads at a premisesupplied electrical power via a common feed. Such a method includesestimating time statistics for power changes in the common power feedusing historical data, based on a relatively “long” time interval;reprocessing the aggregated power change data using those statistics, tocluster tuples of power changes which, statistically, appear likely tobe attributable to the same load; merging similar clusters; separatingoverlapping clusters; updating the time statistics to estimate the timesthe loads appear to be in different states; and, based on the updatedstatistics, processing real-time power-change measurements according tosome of the foregoing steps (reprocessing through updating) to clusterdetected changes and develop real-time load state information.

Embodiments employing such a method may further include associating thereal-time load state information with identifiable loads; andassociating the real-time load state information with identifiable loadsmay comprise correlating known load actions with the estimates.

In embodiments employing any of the foregoing method examples, mergingsimilar clusters may be performed using a modification of a Viterbialgorithm.

According to some embodiments, there is shown a method for nonintrusivemonitoring of electrical energy usage by a plurality of electrical loadsat a premise supplied electrical power via a common feed, comprising,via a sensor, providing a sensor output signal indicative of powerdelivered through the feed over a time interval; monitoring the sensoroutput signal to detect positive and negative changes of power, powersurge amplitudes and durations; clustering negative changes of power;matching negative and positive changes of power; estimating times loadswere turned on and turned off during an interval of interest; andstatistically characterizing the operation of at least one of saidloads.

In some embodiments, a method for nonintrusive monitoring of electricalenergy usage by a plurality of electrical loads at a premise suppliedelectrical power via a common feed, includes monitoring load statechanges and power surges and their statistical distributions are used inorder to more accurately identify loads and their energy consumption.Second, statistics of time of use (in terms of both duration and time ofday) are utilized for better appliance identification and matching withenergy consumption. Third, the matching between the measured powerobservations and the appliances at the premise is made by considerationof those series of transitions among the appliance states which arepossible, which maximizes the likelihood of correctly determining notonly the given series of power changes but also the time-of-usestatistics and power surge statistics.

In some embodiments a method is provided for nonintrusive monitoring ofelectrical energy usage by a plurality of electrical loads at a premisesupplied electrical power via a common feed, comprising: via a sensor,providing a sensor output signal indicative of power delivered throughthe feed over a first time interval; monitoring the sensor output signalto detect positive and negative changes of power, power surge amplitudesand durations; clustering negative changes of power; matching negativeand positive changes of power; estimating times loads were turned on andturned off during an interval of interest; and statisticallycharacterizing the operation of at least one of said loads. Clusters maybe sorted according to their mean values, a Viterbi algorithm then maybe applied to n-tuples of said clusters; cluster conflicts are thenresolved to provide a set of clusters disambiguating power changes; andappliance states are estimated based on the power changes represented bysaid set of clusters. Such a method also my involve updating clusteringand appliance feature statistics based on the results of the previousoperations. In some embodiments, for a second time interval shorter thanthe and later than the first time interval, the steps of sorting throughestimating may be re-performed on clusters created from power changessensed by the sensor during the second time interval.

In some embodiments, a method may be practiced for nonintrusivemonitoring of electrical energy usage by a plurality of electrical loadsat a premise supplied electrical power via a common feed, comprising:detecting aggregate load state changes and power surges and theirstatistical distributions; and matching detected power observations andthe appliances at the premise by consideration of those series oftransitions among the appliance states which are possible andeliminating from consideration state changes which are not permitted orare statistically improbable to maximize the likelihood of correctlydetermining the loads to which the detected series of power changespertain.

Another aspect of the invention, appearing in some embodiments, is asystem for nonintrusive monitoring of electrical energy usage by aplurality of electrical loads at a premise supplied electrical power viaa common feed, comprising: a power sensor configured and arranged tomonitor aggregate power consumed at the premise; means for detectingchanges in the monitored power; and a processor executing stored programinstructions to disambiguate the detected power changes and associatethem with individual loads by clustering power changes and, by means ofa Viterbi algorithm, matching clusters to identify power changesassociated with individual loads.

BRIEF DESCRIPTION OF THE DRAWINGS

A set of drawing figures is provided, to be reviewed in conjunction withthe detailed description of some embodiments, for a fuller understandingthereof. Like reference designations in the figures are intended torefer to the same or corresponding elements. In the drawings:

FIG. 1 is a block diagram of a system according to inventive conceptsset forth herein and in which the herein-disclosed methods may beemployed;

FIG. 2 is a high-level diagrammatic illustration of informationprocessing according to herein-disclosed inventive concepts;

FIG. 3 is a flow chart depicting an example embodiment of preliminarystage information processing of historical power change data accordingto a herein-disclosed method for disaggregating power changes;

FIG. 4 is an example of an aggregated power consumption signal from asensor as discussed herein, for purposes of identifying a typicalnegative power change;

FIG. 5 is an example of a typical positive power change in an aggregatedpower consumption signal from a sensor as discussed herein, for purposesof identifying a typical power surge;

FIG. 6 is a set of three views of example adjacent clusters, A-C, oftypical power change frequency profiles, their corresponding hourlypresence in time functions D-F and the resulting cluster merger profile,G;

FIG. 7 is a flow chart of an example of a typical “main” algorithmaccording to these teachings, used first on historical data and then toprocess real-time or near real-time power change data; and

FIG. 8 is an illustration of an example of cluster states as a functionof time, showing how the application of one of the concepts presentedherein can be used to exclude from a cluster a state not appearing intwo adjacent cluster pairs.

DETAILED DESCRIPTION OF EMBODIMENTS

Attention is now directed to FIGS. 1-7, which illustrate an embodimentof a system and method for practicing aspects of the inventive conceptsdisclosed herein. In embodiments according to these drawing figures, itis presumed that the loads are limited to those with only two states,“on” and “off.” Later, extension of the discussed examples to loadshaving multiple power-consuming states will be disclosed. However, in acommercial premise, it is reasonable to expect the majority of loads tobe of the two-state type, such as lighting and devices in the heating,ventilation and air conditioning (HVAC) systems, such as compressors,fans and heating apparatus. So initially limiting discussion totwo-state loads still includes a large category of uses.

With reference to FIG. 1, a sensor 10 is connected to monitor anelectrical power feed line 12 such as a service feed to a residential orcommercial premise 14. Power is distributed within premise 14 to anumber of loads such as loads 16A, 16B and 16C, through a service panel17. The sensor may be of conventional design and should be one thatprovides an output signal that varies according to aggregate energy flowin the feed line. The output signal may be an analog voltage or currentor a digital value. Alternatively, in some embodiments a sensor may beemployed that is responsive to, or outputs a signal indicative ofcurrent, current changes or voltage changes on the feed line (e.g., at aservice entry point), though a signal indicative directly of power ispreferable. In some embodiments, the sensor may be integrated into anelectrical energy consumption meter such as a utility provider mayemploy to measure and bill for energy usage. Sensor 10 delivers itsoutput signal, directly or indirectly (e.g., via an analog-to-digitalconverter, not shown, if the sensor output signal is in analog form) toa processor 18 (e.g., a microprocessor), which executes stored programinstructions from a non-transitory storage medium 19, to implementsignal processing methods as discussed below. Processor 18 and storagemedium 19 are shown as being situated at the premise 14 but this is notnecessary. They could just as well be remotely located provided thesensor 10 is coupled to an appropriate communication mechanism to feedits output via a communication interface and a communications medium,wired and/or wireless, to the remote processor. For example, the sensormight employ a power line communications network to send its output tothe processor.

FIGS. 2-7 illustrate an exemplary method for processing changes inaggregate energy consumption (or, to be more precise, instantaneouspower delivery) via a premises electrical utility service cable.

Turning first to FIG. 2, there is shown conceptually the flow ofinformation according to the methodology described herein. A sensor suchas sensor 10 produces data 22. This data is analyzed to extract threetypes of information: detected changes of power levels, 24A; power surge(transient) amplitudes, 24B, and power surge durations, 24C. Thatinformation is processed using processor 18 to execute signal processingmethods (algorithms) 26 described below, to produce disaggregated loadsignals 28.

The signal processing methods 26 may have three stages: a preliminaryprocessing stage, a main stage in which historical power usage for thepremise is analyzed, and a real-time stage in which the same techniquesare used as in the main stage but in which near real-time data isprocessed.

Preliminary Processing

As shown in FIG. 3, the preliminary stage 30 of the signal processingmethod (algorithm) starts with analyzing and modeling historical dataabout power usage at the premise, i.e. - the data collected by a sensorover a significant interval, e.g., a two-week interval. Step-wisechanges of power consumption are firstly identified, step 32, and themagnitude of positive and negative changes are estimated. Step 33.Initial emphasis is on negative changes of power consumption (i.e.,sudden drops) (see the drop A, for example, in FIG. 4). These negativechanges indicate a reduction in energy consumption and usuallycorrespond to an appliance being turned off (or, in the case of loadsoperable in multiple states, to an appliance changing its operatingstate from one “on” state to another “on” state; such loads will beaddressed below).

For positive changes in power consumption, note that some appliancespull a surge of power to start. Therefore, erroneous readings for themagnitude of the change may occur unless a post-surge value is used forthe positive power change. FIG. 5 shows an example of a surge 52 and ofthe post-surge power change 54. The surge, or transient, 56, ischaracterized by its magnitude (ΔP_(surge)) and duration (Δt_(surge)).The surge magnitude and duration are estimated in step 34.

Due to measurement errors and natural variability of conditions, themeasured negative change of power when a given appliance is turned offwill not be single-valued, but will be distributed (scattered) about anominal value. Therefore, in order to identify appliances, theidentified negative changes of power are grouped into clusters, step 36,using an appropriate statistical method, e.g., the well-known andpopular ISODATA clustering algorithm (see, e.g., Tou, J. T., PatternRecognition Principles, New York, Addition-Wesley, 1974, herebyincorporated by reference, or other references). Each such cluster maycorrespond to a separate appliance being turned off. The positivechanges of power are not clustered at this stage.

The clustering procedure can result in errors, of course. A singleappliance can yield both positive and negative power changes thatcorrespond to multiple identified clusters. Those clusters then need tobe merged in order to have a complete record for that appliance.Additionally, multiple appliances can correspond to a single cluster,which then needs to be split.

Merging of clusters based on negative power changes occurs in steps 38and 40. For cluster merging, the empirical statistics of appliance usagein time are calculated. The statistics can be, for example, the hourlypresence or absence of a negative change of power for a given cluster.That is, a binary variable or function may be defined which denoteswhether a negative change of power occurred during each hour. If atleast one negative change of power within the boundaries of a givencluster occurred during a given hour, then the function of hourlypresence for that cluster at the given hour may be assigned the value“1”. Otherwise, the function of hourly presence for that cluster at thegiven hour is assigned the value “0.” The degree of similarity of loadusage between cluster pairs is then estimated. Step 38. This may bedone, for example, by calculating a fraction of hours during which bothclusters are present (i.e., their functions of hourly presence both havea value of 1). Then adjacent cluster pairs whose degree of load usagesimilarity exceeds a threshold are merged. Step 40.

FIG. 6 shows an example of cluster merging. Three clusters (A-C) shownin the Figure are adjacent clusters identified by the aforementionedISODATA algorithm. They all have similar hourly presence in time (D-F onFIG. 6). Therefore, they are merged together (G).

After merging, the clusters are numbered in the order of their meanvalues. In each cluster, the negative power changes are characterizedstatistically in parametric form, e.g., by fitting their empiricaldistribution to a Gaussian mixture model (Tou, 1974) or to a Laplacedistribution mixture. Experience suggests that a two-component Gaussianor Laplace mixture model of the probability density function (PDF) issufficient in most cases; however, other parametric distribution modelscan be used. Note that the cluster boundaries may overlap.

Preliminary time statistics of appliances being in states “on” and “off”are then estimated. Step 42. To this end, each identified negative powerchange j of magnitude −ΔP_(ij) that occurred at time t_(j) and came fromcluster i (i=1, 2, . . . , n, where n is the total number of clustersafter merging), is matched with a positive power change k of magnitudeΔP_(ik) that occurred earlier, at time t_(k). Step 44. An exact equalitybetween the positive and negative power changes for a match is notrequired, instead, a tolerance δ is used:ΔP_(ik) εΔP_(ij)(1±δ).  Eq. 1At this stage, the match is considered to be the first ΔP_(ik)satisfying Eq. (1) when going backward in time from the −ΔP_(ij). Inthis way, for each cluster i, a sample set of intervals or times “on”{t_(on)}, is constructed by calculating t_(on)=t_(j)−t_(k) for eachavailable matching pair. Similarly, a sample set of intervals or times“off” {t_(off)}_(i) is constructed by calculatingt_(off)=t_(k+1)−t_(j). Step 46. Once both sample sets are available foreach cluster, the cumulative distribution functions (CDF) of t_(on) andt_(off) for each cluster are calculated. Step 42. (Other time-dependentstatistics, e.g., the clock-time probability of use, can also beimplemented for cluster characterization.)

A collection of the positive power changes that match the negative powerchanges from cluster i is considered to be cluster i_(plus). In eachsuch cluster, the statistical distribution of the positive power changesis parametrically characterized, e.g., by fitting the empiricaldistribution to a two-component Gaussian or Laplace mixture. In eachcluster i_(plus), the surges are also statistically characterized. Thesurge magnitude (ΔP_(surge)) and duration (Δt_(surge)) are used toobtain a sample set of surge magnitudes and a sample set of surgedurations for cluster i_(plus). Then, the PDFs of ΔP_(surge) andduration Δt_(surge) for each cluster are fitted, e.g., to a Gaussianmixture model. Table 1 summarizes the statistics that preferably areobtained in the preliminary processing. Note, that the waveform signalfeatures obtainable at a higher sampling rate can also be included inTable 1 in a similar manner and included into the main algorithmdescribed in the next section.

TABLE 1 Cluster i characteristic Statistical characterization Negativechange of power, W Parametric PDF (Gaussian or Laplace mixture),P_(i(−)) Positive change of power, W Parametric PDF (Gaussian or Laplacemixture), P_(i(+)) Time on, s CDF (non-parametric), C_(on,i) Time off, sCDF (non-parametric), C_(off,i) Surge magnitude, W Parametric PDF(Gaussian or Laplace mixture), s_(m,i) Surge duration, s Parametric PDF(Gaussian or Laplace mixture), s_(d,i) Presence in time Binary functionof clock time, B_(i)

Main Process for Historical Data

The main process is intended to better match the negative and positivechanges of power and resolve ambiguities relating to the simultaneousstarting or stopping of two or more appliances, measurement/processingerrors, and the overlap between adjacent clusters. This process works asfollows.

Consider adjacent clusters of negative power changes i and i+1. Each ofthese clusters includes the detected negative power changes that rangefrom −ΔP_(i) _(_) _(max) to −ΔP_(i) _(_) _(min) and from −ΔP_(i+1) _(_)_(max) to −ΔP_(i+1) _(_) _(min) for clusters i and i+1 correspondingly.Note that, because of the potential overlap −ΔP_(i) _(_)_(min)≠−ΔP_(i+1) _(_) _(max). The information pertinent to theseclusters also includes the hourly usage statistics and the time on/timeoff statistics.

Consider the detected positive power changes. The positive power changesΔP_(k) are considered to be candidates for matching with the clusters ior i+1 if they are within the matching boundaries plus the tolerance:ΔP _(i+1,min)(1−δ)≦ΔP _(k) ≦ΔP _(i,max)(1+δ)  Eq. 1

Note that the boundaries, Eq. (2), are generally broader than thosecorresponding to the positive clusters i_(plus) and (i+1)_(plus).

Clusters i and i_(plus) presumably correspond to appliance i, whereasclusters i+1 and (i+1)_(plus) correspond to appliance i+1. Since each ofthe appliances i and i+1 can either be in the “on” or “off” states, thetotal number of states in the system that includes both appliances isfour. These states are listed below.

TABLE 2 State Appliance i Appliance i + 1 1 off off 2 on off 3 off on 4on on

The system with the states shown in Table 2 can transition from onestate to another as soon as a new power change within the boundaries isrecorded. The states and the transitions within these states are hiddenfor an observer, whereas the changes of power are observable. Thesequence of transitions of the system is directly related to thesequence of the observations, and the current system state depends onthe previous state through transition probabilities. Therefore, thissystem can be represented by a hidden Markov model (HMM) and the hiddenpath of state transitions can be estimated by a well-known Viterbialgorithm.

Tables 3 (positive change ΔP with a surge) and 4 (negative change) listthe probabilities in terms of Tables 1 and 2.

TABLE 3 Transition between states Probability 1 → 1 0 1 → 2$\frac{\alpha_{12}}{\alpha_{12} + \alpha_{13}},{\alpha_{12} = {{P_{i{( + )}}\left( {\Delta\; P} \right)}{s_{m,i}\left( {\Delta\; P_{surge}} \right)}{s_{d,i}\left( {\Delta\; t_{surge}} \right)}\Delta\;{{C_{{off},i}\left( t_{12} \right)}\left\lbrack {1 - {C_{{off},{i + 1}}\left( t_{13} \right)}} \right\rbrack}}}$1 → 3 $\begin{matrix}{\frac{\alpha_{13}}{\alpha_{12} + \alpha_{13}},{\alpha_{13} = {{P_{i + {1{( + )}}}\left( {\Delta\; P} \right)}{s_{m,{i + 1}}\left( {\Delta\; P_{surge}} \right)}{s_{d,{i + 1}}\left( {\Delta\; t_{surge}} \right)}\Delta\;{{C_{{off},{i + 1}}\left( t_{13} \right)}\left\lbrack {1 -} \right.}}}} \\\left. {C_{{off},i}\left( t_{12} \right)} \right\rbrack\end{matrix}$ 1 → 4 0 2 → 1 0 2 → 2 0 2 → 3 0 2 → 4 1 3 → 1 0 3 → 2 0 3→ 3 0 3 → 4 1 4 → 1 0 4 → 2 0 4 → 3 0 4 → 4 0

TABLE 4 Transition between states Probability 1 → 1 0 1 → 2 0 1 → 3 0 1→ 4 0 2 → 1 1 2 → 2 0 2 → 3 0 2 → 4 0 3 → 1 1 3 → 2 0 3 → 3 0 3 → 4 0 4→ 1 0 4 → 2$\frac{\alpha_{42}}{\alpha_{42} + \alpha_{43}},{\alpha_{42} = {{P_{i{( - )}}\left( {{- \Delta}\; P} \right)}\Delta\;{{C_{{on},{i + 1}}\left( t_{42} \right)}\left\lbrack {1 - {C_{{on},i}\left( t_{43} \right)}} \right\rbrack}}}$4 → 3$\frac{\alpha_{43}}{\alpha_{42} + \alpha_{43}},{\alpha_{43} = {{P_{i{( - )}}\left( {{- \Delta}\; P} \right)}\Delta\;{{C_{{on},i}\left( t_{43} \right)}\left\lbrack {1 - {C_{{on},{i + 1}}\left( t_{42} \right)}} \right\rbrack}}}$4 → 4 0

The transition probabilities listed in Tables 3 and 4, along with theestimated statistics listed in Table 1, can be applied to the series ofpositive and negative power changes through the Viterbi-type algorithm.However, those skilled in the art will conclude from observation ofTables 3 and 4 that there are two peculiarities that may hamper theimplementation of the Viterbi-type algorithm. First, several transitionsbetween the states are forbidden, which may render the algorithmunsolvable. Second, the transition probabilities of this system aretime-dependent, which calls for additional calculations of the timeintervals t₁₂, t₁₃, t₄₂ and t₄₃. The time-dependent probabilities alsomake the current system state dependent on several previous states andnot on just one previous state. The algorithm will be unsolvable, e.g.,in case of a missing power change or in case of a wrong power change,which in turn can be, e.g., the result of a simultaneous starting orstopping of two or more appliances or a measurement/processing error.The missing power change can result, e.g., from a ramping up of powerconsumption when an appliance starts up, so that the power change getssplit. In case of such insolvency, the method can be adapted in such away as to yield a special state, e.g., 0, each time the insolvencyoccurs. After the historical data has been processed for the clusters iand i_(plus), these special state occurrences can be found and thecorresponding power changes can be separated and excluded for furtherconsideration. The procedure then is reapplied to the remaining data.The foregoing process can be repeated several times until the number ofthe insolvencies is below a pre-defined threshold.

The procedure is firstly applied to clusters 1 and 2, then to clusters 2and 3, . . . , n−1, n. In this way, every cluster but the first and then^(th) will be processed twice. For each cluster k, k=2, 3, . . . , n−1,the series of its states obtained by the above process to the pair k−1,k is compared to that obtained for clusters k, k+1. Since the mainpurpose of the process for historical data is better separation ofclusters, those states of cluster k that do not appear in bothalgorithmic solutions are excluded, together with the earlier consideredstates resulting in insolvency. FIG. 8 gives an example of suchexclusion. The state of cluster 2 when paired with cluster 1 at X (afirst solution) does not coincide with that at Y when cluster 2 ispaired with cluster 3 (a second solution). Hence, the states X and Y areexcluded.

Another strategy for dealing with the missing power changes can beconsideration of non-zero probability of the system to remain in thesame state. This strategy is also applicable to the problem ofoverlapping clusters, in which case there are “foreign” power changes,i.e., the changes that came from the adjacent clusters. If theprobabilities of transitions 1→1, 2→2, 3→3, 4→4 (see Tables 3, 4) arenon-zero, then a missing power change will no longer cause the system toremain in the previous state. This probability is proportional to theprobability of an appliance (called an “external” appliance), other thanthe two considered appliances, being turned on or off and producing anobserved power change ΔP or larger. Analogously, the presence of theforeign power changes will make the probabilities of all otherpreviously forbidden transitions to be non-zero. Therefore, thetransition probability matrix may be modified to account for thetransitions from “external” appliances.

The transition probability matrix with the possibility of such externaltransitions is listed in Table 5 for negative changes of power. A matrixfor positive power changes with the external transitions can be obtainedsimilarly. The exact probabilities can be straightforwardly calculatedsimilarly to the calculations underlying Tables 2 and 3.

TABLE 5 Transition between states Probability 1 → 1 point from externalcluster 1 → 2 missing point from state 2 AND point from external cluster1 → 3 missing point from state 3 AND point from external cluster 1 → 4 2missing points (states 2 AND 3) AND point from external cluster 2 → 1 ∝w_(i+1)P_(i(−))(−ΔP)ΔC_(on,i)(t₂₁)[1 − C_(off,i+1)(t₂₄)] 2 → 2 pointfrom external cluster 2 → 3 missing point from state 4 AND is 4→3transition 2 → 4 missing point from state 3 AND point from externalcluster 3 → 1 ∝ [w_(i+1)P_(i(−))(−ΔP)[1 −C_(off,i)(t₃₄)]ΔC_(on,i+1)(t₃₁)] 3 → 2 missing point from state 4 AND is4→2 transition 3 → 3 point from external cluster 3 → 4 missing pointfrom state 4 AND is 4→2 transition 4 → 1 missing point (states 2 OR 3)AND is (2→1 OR 3→1) transition 4 → 2 ∝w_(i+1)P_(i(−))(−ΔP)ΔC_(on,i+1)(t₄₂)[1 − C_(on,i)(t₄₃)] 4 → 3 ∝w_(i)P_(i(−))(−ΔP)ΔC_(on,i)(t₄₃)[1 − C_(on,i+1)(t₄₂)] 4 → 4 point fromexternal cluster

The processing technique under this strategy can take several forms. Forexample, the processing can be done in triplets (e.g., clusters i, i−1,and i+1) or even larger clusters, for more accuracy, considering thecluster as an n-tuple of points, where n is the number of points (powerchanges) in the cluster. At each triplet (i.e., 3-tuple), the pairs i,i−1 and i, i+1 are firstly independently processed as described above.Then the points of no state change are identified. Such points in thefirst pair, if they match those identified in the second pair, areexcluded from consideration in the first pair, and the modified Viterbialgorithm is reapplied to the first pair. The same processing next isapplied to the second pair. After this processing, the information onpoints belonging to cluster i is fused from the two pairs using themaximum probability principle. That is, if point # k was identified asbelonging to cluster i in both pairs, it is accepted as belonging tocluster i. If point # k was found to belong to cluster i in the firstpair (or in the second pair), but to belong to cluster i+1 in secondpair (or to i−1 in first pair), the probabilities of these twopossibilities are compared. If the first possibility has a higherprobability, point # k is concluded to belong to cluster i.

After all pairs of clusters have been processed, the power changescorresponding to the excluded or separated states are considered.Various strategies can be applied to processing these power changes. Forexample, if several excluded power changes occur within a given timeinterval, they can be merged together. Isolated-in-time power changescan be split: ΔP=ΔP₁±ΔP₂, where ΔP₁ and ΔP₂ are within the boundaries ofany two clusters. The algorithm is then reapplied to the power changedata modified in this way.

After the successive algorithm processing of the historical data, thestatistical characteristics of the clusters (see Table 1) are updated.Each obtained empirical distribution of times on/off is thenstatistically tested for multi-modality. If significant multi-modalityis detected, then the corresponding clusters preferably are split, e.g.,using clustering of the times that have exhibited the bimodality.

Once the clustering of the power changes has been finalized, theclusters can be named by corresponding appliances using, e.g., theinformation of the power draw and usage patterns.

Main Algorithm for Near Real-Time Data

Once historical data has been processed to establish startingstatistics, power usage is monitored in real-time or near real-time,using substantially the same methodology. However, instead ofconsidering data over a lengthy time period, a data window of a shorterreasonable size, e.g., the most recent 24 hours, is used. Each time anew power change is detected, it is processed as previously described.

Since the algorithm is intended to resolve the likeliest state path,i.e., the most probable sequence of appliances' states, the appliancestates estimated at a given time will be re-estimated as soon as newdata are obtained and processed.

In the example embodiments discussed above, a modified Viterbi algorithmwas used for pairs of appliances, instead of applying it simultaneouslyto the N appliances at a premise. By doing so, the interactions betweenappliance (cluster) i and i±3, i±4, i±5, etc. are essentially neglected.This is because the overlap in power draw between them is supposed to besmall. On this account, computational complexity becomes linearlyproportional to the number of appliances, whereas the conventional useof a Viterbi algorithm would result in an exponential dependence. Whenthe overlap between cluster i and i+3 is not negligible, one mayconsider using triples instead of pairs. In a triple, the number ofstates would be 2^3=8 and number of transitions=64, which is stillmanageable. If triplets are not enough, then quadruplets and so on canbe used. In any case, by decomposing of the whole system into such smallunits, the computational complexity is decreased by many orders ofmagnitude.

Having described inventive concepts as well as some example embodimentsin detail, various modifications and improvements will readily occur tothose skilled in the art. Such modifications and improvements areintended to be within the spirit and scope of the invention.Accordingly, the foregoing description is by way of example only, and isnot intended as limiting. The invention is limited only as defined bythe following claims and the equivalents thereto.

What is claimed is:
 1. A method for nonintrusive monitoring of electrical energy usage by a plurality of electrical loads at a premise to which electrical power is supplied via a common feed, comprising: clustering, using at least one processor, tuples of power changes in the electrical energy usage at the premise that are attributable to a same load of the plurality of electrical loads at the premise, wherein the clustering comprises analyzing power changes in the electrical energy usage based on usage statistics for the plurality of electrical loads to identify power changes attributable to the same load; calculating, using the at least one processor, a degree of similarity between clusters of tuples of power changes based at least in part on times associated with power changes in the clusters; merging, using the at least one processor, clusters of tuples of power changes having a degree of similarity above a threshold; updating, using the at least one processor, the usage statistics to estimate times different loads of the plurality of electrical loads are in different states; and based on the updated usage statistics, processing, using the at least one processor, real-time power-change measurements to develop real-time load state information based on detected power changes in the electrical energy usage.
 2. The method of claim 1 further including associating the real-time load state information with identifiable loads of the plurality of electrical loads at the premise.
 3. The method of claim 2, wherein associating the real-time load state information with identifiable loads comprises correlating known load actions with the updated usage statistics.
 4. The method of claim 1 wherein calculating the degree of similarity between clusters and merging clusters based on the degree of similarity comprises applying a Viterbi algorithm to analyze power changes that may be associated with state transitions of known loads, wherein applying the Viterbi algorithm comprises analyzing power changes based at least in part on transition probabilities between states of the known loads.
 5. A method for nonintrusive monitoring of electrical energy usage by a plurality of electrical loads at a premise to which electrical power is supplied via a common feed, comprising: a. via a sensor, providing a sensor output signal indicative of power delivered through the feed over a first time interval; b. monitoring, using at least one processor, the sensor output signal to detect positive and negative changes of power, power surge amplitudes and durations; c. clustering, using the at least one processor, negative changes of power, wherein clustering negative changes in power comprises: clustering, using the at least one processor, tuples of power changes in the electrical energy usage at the premise that are attributable to a same load of the plurality of electrical loads at the premise, wherein the clustering comprises analyzing power changes in the electrical energy usage based on usage statistics for the plurality of electrical loads to identify power changes attributable to the same load; calculating, using the at least one processor, a degree of similarity between clusters of tuples of power changes based at least in part on times associated with power changes in the clusters; and merging, using the at least one processor, clusters of tuples of power changes having a degree of similarity above a threshold; d. matching, using the at least one processor, negative and positive changes of power; e. estimating, using the at least one processor, times loads were turned on and turned off during a second time interval; and f. statistically, using the at least one processor, characterizing the operation of at least one of said loads.
 6. The method of claim 5, wherein: the clustering further comprises: g. sorting clusters according to their mean values; h. applying a Viterbi algorithm to tuples of clusters; and i. resolving cluster conflicts to provide a set of clusters disambiguating power changes; and the method further comprises: j. estimating appliance states based on the power changes represented by said set of clusters.
 7. The method of claim 6, further comprising updating clustering and appliance feature statistics based on the results of steps i and j.
 8. The method of claim 7, further comprising, for a second time interval shorter than and later than the first time interval, re-performing steps g-j on clusters created from power changes sensed by the sensor during the second time interval.
 9. A system for nonintrusive monitoring of electrical energy usage by a plurality of electrical loads at a premise to which electrical power is supplied via a common feed, comprising: a. a power sensor configured and arranged to monitor aggregate power consumed at the premise; b. means for detecting changes in the monitored power; and c. a processor executing stored program instructions to disambiguate the detected power changes and associate them with individual loads by clustering power changes and, by means of a Viterbi algorithm, matching clusters to identify power changes associated with individual loads, wherein clustering the power changes comprises: clustering tuples of power changes in the electrical energy usage at the premise that are attributable to a same load of the plurality of electrical loads at the premise, wherein the clustering comprises analyzing power changes in the electrical energy usage based on usage statistics for the plurality of electrical loads to identify power changes attributable to the same load; calculating a degree of similarity between clusters of tuples of power changes based at least in part on times associated with power changes in the clusters; and merging clusters of tuples of power changes having a degree of similarity above a threshold.
 10. The method of claim 1, further comprising calculating the usage statistics based for the plurality of electrical loads, for use in the clustering, based on an analysis of the electrical energy usage at the premise. 